Mathematical Modelling and Optimization of Medication Regimens for Combination Immunotherapy of Breast Cancer

Immunotherapy is an emerging and effective treatment for cancer. The mRNA-based cancer vaccines enhance the immune response to cancer cells by activating T cells. However, the cytotoxic T-lymphocyte antigen (CTLA-4) receptor signaling inhibits T-cell activation, thereby reducing the effectiveness of the mRNA-based vaccines. Fortunately, the anti-CTLA-4 monoclonal antibody therapy can block CTLA-4 signaling. Nevertheless, the use of anti-CTLA-4 antibodies is also accompanied by immunotoxic side effects. Therefore, an effective and safe medication regimen plays an essential role in the treatment of cancer. First, we develop a mathematical model to describe the interaction of mRNA-based cancer vaccines and anti-CTLA-4 antibodies under the tumor immune microenvironment. Secondly, by employing the method of Markov Chain Monte Carlo (MCMC), the model is parameterized using experimental data, and the simulations are in agreement with experimental results. Finally, the gradient descent method is designed to optimize the medication regimens to inhibit tumor growth and reduce the side effects. Additionally, we find that the anti-CTLA-4 antibody should be administered following vaccination, and the dose of the antibody should positively correlate with the dose of vaccine within a safe range. Our study provides a theoretical basis for the selection of treatment regimens for clinical trials from a mathematical perspective.